turunan pertama dari f(X)=3X^2/2X+1 adalah=

Bab Turunan

f(x) = 3x^2/(2x + 1)
Misalkan
f(x) = u/v
Maka
f'(x) = (u'v - uv')/v^2

u = 3x^2
u' = 6x

v = 2x + 1
v' = 2

f'(x) = (6x(2x + 1) - 2(3x^2))/(2x + 1)^2
f'(x) = (12x^2 + 6x - 6x^2)/(4x^2 + 4x + 1)
f'(x) = (6x^2 + 6x)/(4x^2 + 4x + 1)

f(x) = 3x^2 / (2x + 1) = u/v
u = 3x^2 => u' = 6x
v = (2x + 1) => v' = 2
f'(x) = (u' v - v' u) / v^2
= (6x (2x + 1) - 2 (3x^2)) / (2x + 1)^2
= (12x^2 + 6x - 6x^2) / (2x + 1)^2
= (6x^2 + 6x) / (2x + 1)^2

= 6x(x + 1) / (2x + 1)^2